in this paper we investigate the generalized hyers-ulamstability of the following cauchy-jensen type functional equation$$qbig(frac{x+y}{2}+zbig)+qbig(frac{x+z}{2}+ybig)+qbig(frac{z+y}{2}+xbig)=2[q(x)+q(y)+q(z)]$$ in non-archimedean spaces

The problem of compensation of infinite-dimensional actuator or sensor dynamics of more complex type than pure delay was solved recently using the backstepping method for PDEs. In this paper we construct an explicit feedback law for a multi-input LTI system which compensates the wave PDE dynamics in its input and stabilizes the overall system. Our design is based on a novel infinite-dimensional...

A dynamic inversion compensation scheme is presented for backlash. The compensator uses the backstepping technique with neural networks (NN) for inverting the backlash nonlinearity in the feedforward path. Instead of a derivative, which cannot be implemented, a filtered derivative is used. Full rigorous stability proofs are given using filtered derivative. Compared with adaptive backstepping co...

This paper deals with the tracking control design for systems governed by linear parabolic partial differential equations with spatially and temporally varying coefficients and boundary input. For the boundary feedback control the backstepping method is applied, which allows to determine an exponentially stabilizing state feedback controller such that the closed-loop system behaves in the nomin...

The backstepping technique was used in order to synthesise a non-linear control law for the non-linear model of the power plant station. The non-linearities in the model are related to steam flow through the super-heater and action of turbine valves. The time constant of the boiler is considered as an unknown parameter. Its value has to be adapted. The backstepping procedure presents a straight...

A nonlinear dynamic output feedback control method for a 5-degree-offreedom AMB is presented in this paper. This method is based on the system structure of AMB and a quadratic-like Lyapunov function. It is shown that backstepping and completing square techniques enable the construction of the voltage input by using measured output only. The control law guarantees the asymptotic stability of the...

In this paper, we present a global adaptive output feedback control scheme for a class of uncertain nonlinear systems to which adaptive observer backstepping method may not be applicable directly. The allowed output feedback structure includes quadratic dependency of the unmeasured states and output-dependent nonlinearities appearing not only additively, but also multiplicatively. Our novel des...

In this study, an adaptive Neural Network (NN) based backstepping controller is proposed to realize chaos synchronization of two gap junction coupled FitzHugh-Nagumo (FHN) neurons with uncertain time delays. In the designed backstepping controller, a simple Radial Basis Function (RBF) NN is used to approximate the uncertain nonlinear part of the error dynamical system. The weights of the NN are...

Backstepping design is proposed to control a Lorenz chaotic system. A major advantage of this method is that it has the flexibility to build the control law by avoiding cancellations of useful nonlinearities. Consequently, the goals of stabilization of chaotic motion and tracking of a reference signal are achieved with a reduced control effort. A comparison with the differential geometric metho...

Abstract To address the problem that attitude of a rigid satellite in orbit is susceptible to external disturbing moments, control method based on backstepping sliding mode proposed, which has strong robustness and anti-disturbance capability. Firstly, coupling term mathematical model eliminated by using method, secondly, law designed reduce sensitivity system disturbance moment change accelera...